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Axial and Vector SFs for L epton -Nucleon Scattering

Arie Bodek University of Rochester Un-ki Yang University of Manchester. Axial and Vector SFs for L epton -Nucleon Scattering. NuFact 11, August 1-6 , Geneva. Neutrino Cross Section. Quasi-Elastic / elastic (W=M): n m + n m - + p by form factors

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Axial and Vector SFs for L epton -Nucleon Scattering

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  1. ArieBodek University of Rochester Un-ki Yang University of Manchester Axial and Vector SFs forLepton-Nucleon Scattering NuFact11, August 1-6, Geneva

  2. Neutrino Cross Section • Quasi-Elastic / elastic (W=M): nm + nm- + p • by form factors • Resonance (low Q2, W< 2): nm + pm- + p + p • by Rein and Seghal model (overlap with DIS) • Deep Inelastic Scattering: nm + pm- + X • by quark-parton model (non-pQCD effect, high xPDFs) • Describe DIS, resonance within quark-parton model: with PDFS, it is easy to convert (e) into () • Challenges • High xPDFs at very low Q2 • Resonance scattering within quark-parton model • What happens at Q2=0? • Axial vector contribution

  3. mf=M* (final state) q P=M Modeling neutrino cross sections • NNLO pQCD +TM approach: describes the DIS and resonancedata very well: • Bodek-Yang LO approach: (pseudo NNLO) Use effective LO PDFs with a newscalingvariable,xwto absorb target mass, higher twist, missing QCD higher orders

  4. Bodek-Yang Effective LO PDFs Model 1. Start with GRV98 LO (Q2min=0.80) 2.Replace xbj with a new scaling, xw 3. Multiply all PDFs by K factors for photo prod. limit and higher twist [ s(g)= 4pa/Q2 * F2(x, Q2) ] Ksea = Q2/[Q2+Csea] Kval = [1- GD2 (Q2) ] * [Q2+C2V] / [Q2+C1V] motivated by Adler Sum rule where GD2 (Q2) = 1/ [ 1+Q2 / 0.71 ] 4 4. Freeze the evolution at Q2 = Q2min - F2(x, Q2 < 0.8) = K(Q2) * F2(xw, Q2=0.8) 5. Fit all DIS F2(p/D) with low x HERA data, photo-production data

  5. Fit Results on DIS F2(p/D) data • Excellent Fitting: • red solid line: effective LO using xw • black dashed line: xbj F2(p) F2(D)

  6. Low x HERA and NMC data • Fit works at low x

  7. Photo-production data • AdditionalKLWfactor for valence quarks: Kval = KLW*[1- GD2 (Q2) ] * [Q2+C2V] / [Q2+C1V] KLW = (n2+Cn)/n2 This makes a duality work all the way down to Q2=0 (for charged leptons) • Photo-production data with n>1 GeV are included in the fitting

  8. F2 Resonance and FL FL(p) • Predictions are in good agreement with resonance data (not included in the fitting); duality works for electrons and muons for our effective LO PDFs F2(p)

  9. Neutrino cross sections • Effective LO model with w describe all DIS and resonance F2 data as well as photo-production data (Q2=0 limit): vector contribution works well • Neutrino Scattering: • Effective LO model works for xF3? • Nuclear correction using e/mscattering data • Axial vector contribution at low Q2? • Use R=R1998 to get 2xF1 • Implement charm mass effect through xw slow rescaling algorithm for F2, 2xF1, and xF3

  10. Effective LO model for xF3? • Scaling variable, w absorbs higher order effectforF2, but the higher ordereffects for F2 and xF3 are not the same • Use NLO QCD to get double ratio not 1 but indep. of Q2 • Enhance anti-neutrino cross section by 3%

  11. Nuclear Effects: use e/m data Fe/D D/(n+P) UpdatedFe/D Lead/Fe

  12. Axial Vector Structure Functions • Type I: Axial Vector = Vector (A=V) • Type II: • 0.6 was chosen to satisfy the prediction from PCAC by Kulagin, agrees with CCFR/CHROUS data for F2 extrapolation to (Q2=0) • But, the non-zero PCAC component of F2axial at low Q2: purely longitudinal

  13. Comparison with CCFR (Fe), CHORUS (Pb) data • Blue point: CHORUS/theory (type II) • Blue line: theory (type I)/(type II) • Red point: CCFR/theory (type II) nu nubar

  14. Comparison with CCFR(Fe), CHORUS (Pb) data

  15. Test of the Adler Sum Rule • This sum rule should be valid at all values of Q2 Axial Vector

  16. Total cross sections • BY(DIS, W>1.4) + Q.E. + Resonance

  17. Summaryof changes from 2004 • 2004: BY Model (currently implemented in Neutrino Monte Carlo) has V=A and H(x)=1 (same scaling violation in F2 and xF3). It has been used for W>1.8 Gave • 2011: Addition of H(x) correction to xF3 plus axial K factor by PCAC (A=PCAC) to F2 • Change anti-neutrino cross sections by ~6%; better agreement with experimental data • Better agreement in ds/dxdy at low Q2 • Better agreement with the total cross sections • Addition of low W K factor (KLW) extend the validity of model down to W=1.4 GeV, thus providing overlap with resonance models

  18. Summary & Discussions • BY Effective LO model with w describe alle/m DIS and resonance data as well as photo-production data (down to Q2=0): provide a good reference for vector SF for neutrino cross section • ds/dxdy data favor updated BY(DIS) type II model • K factors for axial vectors in BY(DIS) type II model are basedon PCACand could be further tuned with new neutrino data (Q2<0.3, e.g. MINERnA) • BY(DIS) type II model (axial=PCAC) provide a good reference forboth neutrino and anti-neutrino cross sections (W>1.8). Low energy neutrino experiments can normalize their data to our model to extract their flux • Model also works well down to W=1.4 GeV, thus providing overlap with resonance models

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